Despite the recent success of deep learning models for text generation, generating clinically accurate reports remains challenging. More precisely modeling the relationships of the abnormalities revealed in an X-ray image has been found promising to enhance the clinical accuracy. In this paper, we first introduce a novel knowledge graph structure called an attributed abnormality graph (ATAG). It consists of interconnected abnormality nodes and attribute nodes for better capturing more fine-grained abnormality details. In contrast to the existing methods where the abnormality graph are constructed manually, we propose a methodology to automatically construct the fine-grained graph structure based on annotated X-ray reports and the RadLex radiology lexicon. We then learn the ATAG embeddings as part of a deep model with an encoder-decoder architecture for the report generation. In particular, graph attention networks are explored to encode the relationships among the abnormalities and their attributes. A hierarchical attention attention and a gating mechanism are specifically designed to further enhance the generation quality. We carry out extensive experiments based on the benchmark datasets, and show that the proposed ATAG-based deep model outperforms the SOTA methods by a large margin in ensuring the clinical accuracy of the generated reports.